The Mississippi Department of Archives & History has the following history of the unit, which covers their history up through the siege of Vicksburg:

“Sketch History of the 7th Mississippi Battalion.” No author, no date. J. L. Power
Collection, Box 8, Catalog # Z/0100.000, Mississippi Department of Archives and History, Jackson, MS.
http://www.history-sites.com/cgi-bin/bbs62x/mscwmb/webbbs_config.pl?page=1;md=read;id=23195

……….

Absalom J. Farmer

Residence was not listed;
Enlisted on 9/1/1862 as a 1st Lieutenant.
On 9/1/1862 he was commissioned into "A" Co. MS 7th Battn Infantry
He died of disease on 10/6/1864
(Estimated date of enlistment)
Promotions:
* Capt
Other Information:
born in 1829
Buried: Louin Cemetery, Louin, MS

Sources used by Historical Data Systems, Inc.:
- Index to Compiled Confederate Military Service Records
- Supplement to the Official Records of the Union & Confederate Armies
- Mississippi Confederate Grave Registry

…….

Record of Events Company A

Stationed at Camp Little near Saltillo, Mississippi, May 13-
August 31, 1862.
May 3.— This company was organized in Jasper County, Missis-
sippi and marched from there to Quitman, Mississippi, where it
remained.

August 12.— It was transported by cars to Saltillo, Mississippi,
where it remains at the present time.
Stationed at Camp Rodgers near Holly Springs, September-Octo-
ber 1862.
August 31.— This company was marched from Saltillo to Gun-
town, a distance of six miles.
September 11.— It was marched to Iuka, distance of forty-five
miles.
September 20.— It was marched from Iuka to Baldwyn, a dis-
tance of forty miles.
September 26.— Marched from Baldwyn to Ripley, a distance of
twenty-five miles, from Ripley to Corinth, a distance of twenty-
one miles, where it met the enemy. Had an engagement and fell
back to Camp Rodgers near Holly Springs.
Station not stated, November-December 1862.
November 4.— This company was marched from Camp Rodgers
near Lumpkin's Mill to Camp Sloan near Abbeville, a distance of
twelve miles.
November 29.— Was marched from Camp Sloan to Camp
Rodgers near Grenada, a distance of seventy miles.
December 27.— It was marched by railroad to Vaughan Station
on the Central Railroad.
One man not accounted for on last muster; aggregate last
muster was but seventy-eight, should have been seventy-nine.
Stationed at Snyder's Mill, January-February 1863.
This company was marched from Vaughan Station on the
Central Railroad to Yazoo City, a distance of twenty-five miles,
where it took passage on board steamboat for this place, where it
has remained from that date to the present time.
Stationed at Enterprise, Mississippi, June 30-October 31, 1863.
Since last muster this command has been captured at Vicks-
burg, Mississippi and paroled and marched to Enterprise, Missis-
sippi, a distance of 140 miles.

Stationed at Enterprise, Mississippi, November-December 1863.
Since last muster this command has remained stationary at
Enterprise, Mississippi.
Stationed at Dog River Factory, Alabama, January-February
1864.
February 9.— Since last muster this company was moved from
Enterprise, Mississippi to Mobile, Alabama by railway, a distance
of 120 miles.

Note: There are no further Company A muster rolls in the records from which these Records of Events were derived

.............

Absolem J. Farmer, age 32, Company A, 7th Battalion Mississippi Infantry, elected 1st Lieutenant May 3, 1862, captured at Vicksburg, Miss. July 4, 1863, paroled July 7, marched to Enterprise, Miss., 140 miles, reported to Parole Camp August 23, exchanged December 20, 1863, last recorded present at the Jan/Feb, 1864 muster,* wounded at Altoona, Ga. October 5, 1864 recorded as Captain, born in Mississippi, no further records

* This was the last Company A muster roll surviving to be recorded in these records

M269: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Mississippi

….

For further information on the battalion, see:

http://www.mississippiscv.org/MS_Units/7th_Bn_MS_INF.htm